测度链上动力方程两点边值问题多解的存在性
Existence of Multiple Solutions for Second Order Second-Point Boundary Value Problems of Dynamics Equation on Time Scale

作者: 赵梦田 * , 李红玉 :山东科技大学数学与系统科学学院,山东 青岛 ;

关键词: 测度链变号解特征值Time Scale Sign-Changing Solution Eigenvalue

摘要:
利用格结构下的不动点定理,研究了一类测度链上动力方程的两点边值问题 (1) 其中, ,T是[0,1] 上的闭集, 连续,且 。文中结合相应算子的特征值,在非线性项满足次线性条件下,得到此边值问题具有正解,负解和变号解。

Abstract: In this paper, by using the fixed point theorems with lattice structure, we discuss the existence of multiple solutions for the following second-point boundary value problems of dynamics equation on a general time scale. (1) where , Let T be a closed subset of the interval[0,1]  , with , and the function is continuous, with . Combining the eigenvalues of the relevant linear operator, the existence of positive, negative and sign-changing solutions is obtained under the condition that the nonlinear term is sublinear.

文章引用: 赵梦田 , 李红玉 (2016) 测度链上动力方程两点边值问题多解的存在性。 理论数学, 6, 312-317. doi: 10.12677/PM.2016.64046

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